Is there any place that I can find a list of different PDEs and common finite difference schemes used for each? I have seen tables of finite difference coefficients such as the one here http://en.wikipedia.org/wiki/Finite_difference_coefficients, but I realize that studying convergence of a finite difference scheme is a case by case study. Simply replacing the differential operators in a PDE with any arbitrary finite difference operator will not ensure consistency or stability, let alone tell us anything about the dissipation or dispersion in the scheme. So, my question is, does anybody know of a good reference that lists PDEs (common and not-so-common) and the schemes used to solve each (with explanations of the pros and cons to each scheme)?

I'd like to save some work in the future by having a good reference around.

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    $\begingroup$ Having a CFD background, I know some methods for hyperbolic PDE. You can take a look at the following Wiki articles for Lax Friedrichmethod Upwind scheme Crank Nicolson method Lax wendroff method Searching for the names on google should give more results. $\endgroup$ – k1next Feb 21 '13 at 12:20
  • $\begingroup$ For elliptic PDE consider chapter 1. $\endgroup$ – k1next Feb 21 '13 at 12:28
  • $\begingroup$ So, the book that I've been using is Finite Difference Schemes and Partial Differential Equations by Strikwerda. It's a good book, and it has everything that you would need for the basic schemes. But say I have some non-linear PDE or I can't find an appropriate scheme in that book. I'm looking for a list that would make finding appropriate schemes easier. Is this something that would be useful, or am I missing something about how people in numerical methods go about these things. $\endgroup$ – jmbejara Feb 22 '13 at 2:50
  • $\begingroup$ Do you mean a list that tells you for different specified PDE's which method you need to use and why? $\endgroup$ – k1next Feb 22 '13 at 6:02
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    $\begingroup$ How about chapter 2 homepages.cwi.nl/~haverkor/documents/NumMethPDEs.pdf $\endgroup$ – k1next Feb 22 '13 at 12:00

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